Train a nonlinear autoregressive with external input (NARX) neural network and predict on new time series data. Predicting a sequence of values in a time series is also known as多步骤预测. Closed-loop networks can perform multistep predictions. When external feedback is missing, closed-loop networks can continue to predict by using internal feedback. In NARX prediction, the future values of a time series are predicted from past values of that series, the feedback input, and an external time series.

Load the simple time series prediction data.

[X,T] = simpleseries_dataset;

Partition the data into training dataXTrain和TTrain, and data for predictionXPredict. UseXPredict创建闭环网络后执行预测。

XTrain = X(1:80); TTrain = T(1:80); XPredict = X(81:100);

创建一个Narx网络。定义隐藏图层的输入延迟，反馈延迟和大小。

net = narxnet(1:2,1:2,10);

使用时间序列数据使用preparets. This function automatically shifts input and target time series by the number of steps needed to fill the initial input and layer delay states.

[xs，xi，ai，ts] = preparets（net，xtrain，{}，ttrain）;

推荐的做法是将网络完全创建开放循环，然后将网络转换为封闭的循环以进行多步骤预测。然后，闭环网络可以预测您想要的尽可能多的未来值。如果您仅以闭环模式模拟神经网络，则网络可以执行与输入系列中的时间步长一样多的预测。

训练Narx网络。这trainfunction trains the network in an open loop (series-parallel architecture), including the validation and testing steps.

net =火车（net，xs，ts，xi，ai）;

Display the trained network.

查看（网）

Calculate the network outputY, final input statesXf, and final layer statesAfof the open-loop network from the network inputXs, initial input statesXi和初始层状态Ai.

[Y,Xf,Af] = net(Xs,Xi,Ai);

计算网络性能。

perf = perform(net,Ts,Y)

perf = 0.0153

为了预测接下来的20个时间步长的输出，请先在闭环模式下模拟网络。最终输入状态Xf和层状态Af开环网络网络成为初始输入状态xic和层状态Aicof the closed-loop networknetc.

[netc,Xic,Aic] = closeloop(net,Xf,Af);

Display the closed-loop network.

view(netc)

Run the prediction for 20 time steps ahead in closed-loop mode.

Yc = netc(XPredict,Xic,Aic)

Yc=1×20单元格数组列1至5 {[-0.0156]} {[0.1133]} {[-0.1472]} {[-0.0706]} {[-0.0706]} {[0.0355]}列6至10 {[-0.2829]}0.3809]}} {[-0.2836]} {[[0.1886]}列11至15 {[-0.1813]} {[0.1373]} {[0.1373]} {[0.2189]}-0.0156]}} {[0.0724]} {[0.3395]} {[0.1940]} {[0.0757]}